Application of numerical methods to modeling the stellar wind and interstellar medium interaction

We present a review of the application of numerical methods to solve the problem of the stellar/solar wind with the local interstellar medium. Most of approaches described are developed by the authors. They include both purely gas dynamic and magnetohydrodynamic methods. Some attention is given to the influence of the neutral component of the interstellar medium on the flow structure. Far-field boundary conditions are formulated which are usually required in astrophyscal application owing to the extremely large length scale of these problems. Results are presented of the stationary and nonstationary, axisymmetric and geniunly three-dimensional calculations. Newly developed high-resolution numerical methods are discussed which can be applied to a large variety of astrophysical problems. The bibliography includes 113 references. The review will be published in ``CFD Review 97'' by John Wiley.